Helix-coil transition of alanine peptides in water: force field dependence on the folded and unfolded structures

What are the minimal folding seeds in proteins? Experimental and theoretical assessment of secondary structure propensities of small peptide fragments

Certain peptide sequences, some of them as short as amino acid triplets, are significantly overpopulated in specific secondary structure motifs in folded protein structures. For example, 74% of the EAM triplet is found in α-helices, and only 3% occurs in the extended parts of proteins (typically β-sheets). In contrast, other triplets (such as VIV and IYI) appear almost exclusively in extended parts (79% and 69%, respectively). In order to determine whether such preferences are structurally encoded in a particular peptide fragment or appear only at the level of a complex protein structure, NMR, VCD, and ECD experiments were carried out on selected tripeptides: EAM (denoted as pro-'α-helical' in proteins), KAM(α), ALA(α), DIC(α), EKF(α), IYI(pro-β-sheet or more generally, pro-extended), and VIV(β), and the reference α-helical CATWEAMEKCK undecapeptide. The experimental data were in very good agreement with extensive quantum mechanical conformational sampling. Altogether, we clearly showed that the pro-helical vs. pro-extended propensities start to emerge already at the level of tripeptides and can be fully developed at longer sequences. We postulate that certain short peptide sequences can be considered minimal "folding seeds". Admittedly, the inherent secondary structure propensity can be overruled by the large intramolecular interaction energies within the folded and compact protein structures. Still, the correlation of experimental and computational data presented herein suggests that the secondary structure propensity should be considered as one of the key factors that may lead to understanding the underlying physico-chemical principles of protein structure and folding from the first principles.

Conformational Manifold Sampled by Two Short Linear Motif Segments Probed by Circular Dichroism, Vibrational, and Nuclear Magnetic Resonance Spectroscopy

Disordered protein segments called short linear motifs (SLiM) serve as recognition sites for a variety of biological processes and act as targeting signals, modification, and ligand binding sites. While SLiMs do not adopt one of the known regular secondary structures, the conformational distribution might still reflect the structural propensities of their amino acid residues and possible interactions between them. In the past, conformational analyses of short peptides provided compelling evidence for the notion that individual residues are less conformationally flexible than locally expected for a random coil. Here, we combined various spectroscopies (NMR, IR, vibrational, and UV circular dichroism) to determine the Ramachandran plots of two SLiM motifs, i.e., GRRDSG and GRRTSG. They are two representatives of RxxS motifs that are capable of being phosphorylated by protein kinase A, an enzyme that plays a fundamental role in a variety of biological processes. Our results reveal that the nearest and non-nearest interactions between residues cause redistributions between polyproline II and β-strand basins while concomitantly stabilizing extended relative to turn-forming and helical structures. They also cause shifts in basin positions. With increasing temperature, β-strand populations become more populated at the expense of polyproline II. While molecular dynamics simulations with Amber ff14SB and CHARMM 36m force fields indicate residue-residue interactions, they do not account for the observed structural changes.

Rethinking the protein folding problem from a new perspective

One of the main concerns of Anfinsen was to reveal the connection between the amino-acid sequence and their biologically active conformation. This search gave rise to two crucial questions in structural biology, namely, why the proteins fold and how a sequence encodes its folding. As to the why, he proposes a plausible answer, namely, the thermodynamic hypothesis. As to the how, this remains an unsolved challenge. Consequently, the protein folding problem is examined here from a new perspective, namely, as an 'analytic whole'. Conceiving the protein folding in this way enabled us to (i) examine in detail why the force-field-based approaches have failed, among other purposes, in their ability to predict the three-dimensional structure of a protein accurately; (ii) propose how to redefine them to prevent these shortcomings, and (iii) conjecture on the origin of the state-of-the-art numerical-methods success to predict the tridimensional structure of proteins accurately.

The relevance of short peptides for an understanding of unfolded and intrinsically disordered proteins

Over the last thirty years the unfolded state of proteins has attracted considerable interest owing to the discovery of intrinsically disordered proteins which perform a plethora of functions despite resembling unfolded proteins to a significant extent. Research on both, unfolded and disordered proteins has revealed that their conformational properties can deviate locally from random coil behavior. In this context results from work on short oligopeptides suggest that individual amino acid residues sample the sterically allowed fraction of the Ramachandran plot to a different extent. Alanine has been found to exhibit a peculiarity in that it has a very high propensity for adopting polyproline II like conformations. This Perspectives article reviews work on short peptides aimed at exploring the Ramachandran distributions of amino acid residues in different contexts with experimental and computational means. Based on the thus provided overview the article discussed to what extent short peptides can serve as tools for exploring unfolded and disordered proteins and as benchmarks for the development of a molecular dynamics force field.

Randomizing of Oligopeptide Conformations by Nearest Neighbor Interactions between Amino Acid Residues

Flory’s random coil model assumes that conformational fluctuations of amino acid residues in unfolded poly(oligo)peptides and proteins are uncorrelated (isolated pair hypothesis, IPH). This implies that conformational energies, entropies and solvation free energies are all additive. Nearly 25 years ago, analyses of coil libraries cast some doubt on this notion, in that they revealed that aromatic, but also β-branched side chains, could change the ³J(H^NH^Cα) coupling of their neighbors. Since then, multiple bioinformatical, computational and experimental studies have revealed that conformational propensities of amino acids in unfolded peptides and proteins depend on their nearest neighbors. We used recently reported and newly obtained Ramachandran plots of tetra- and pentapeptides with non-terminal homo- and heterosequences of amino acid residues to quantitatively determine nearest neighbor coupling between them with a Ising type model. Results reveal that, depending on the choice of amino acid residue pairs, nearest neighbor interactions either stabilize or destabilize pairs of polyproline II and β-strand conformations. This leads to a redistribution of population between these conformations and a reduction in conformational entropy. Interactions between residues in polyproline II and turn(helix)-forming conformations seem to be cooperative in most cases, but the respective interaction parameters are subject to large statistical errors.

Development and Validation of a DFT-Based Force Field for a Hydrated Homoalanine Polypeptide

A new force field has been created for simulating hydrated alanine polypeptides using the adaptive force matching (AFM) method. Only density functional theory calculations using the Perdew-Burke-Ernzerhof exchange-correlation functional and the D3 dispersion correction were used to fit the force field. The new force field, AFM2020, predicts NMR scalar coupling constants for hydrated homopolymeric alanine in better agreements with experimental data than several other models including those fitted directly to such data. For Ala₇, the new force field shows about 15% helical conformations, 20% conformation in the β basin, and 65% polyproline II. The predicted helical population of short hydrated alanine is higher than previous estimates based on the same experimental data. Gas-phase simulations indicate that the force field developed by AFM solution-phase data is likely to produce a reasonable conformation distribution when hydration water is no longer present, such as the interior of a protein.

Intrinsic Conformational Dynamics of Alanine in Water/Ethanol Mixtures: An Experiment-Driven Molecular Dynamics Study

In vitro, cationic glycylalanylglycine (GAG) forms a hydrogel in binary mixtures of water and ethanol. In water, alanine residue is known for its high polyproline II (pPII) content. Spectroscopic data, including three J-coupling constants and amide I' profiles, indicate that addition of 42% ethanol to water significantly reduces the pPII content of alanine residue in GAG. Here, experiment-based Gaussian Ramachandran distributions of alanine in GAG at different ethanol fractions are examined and three MD force fields are evaluated with respect to their ability to capture these ethanol-induced conformational changes. MD simulations on monomeric GAG in eight different water/ethanol mixtures within Amber ff14SB, OPLS-AA/M, and CHARMM36m reveal that only Amber ff14SB partially captures the ethanol-induced conformational changes of alanine residue in monomeric GAG when 42% ethanol is added to water. MD simulations of 200 mM GAG ensembles in pure water and in the aqueous solution with 42% ethanol showcase the ability of CHARMM36m to capture the effect of ethanol on the average pPII content of alanine in GAG and provide a plausible explanation for this effect, which may stem from an increased propensity of GAG to form oligomers in the presence of ethanol.

Thermodynamics of Helix formation in small peptides of varying lengthin vacuo, implicit solvent and explicit solvent: Comparison between AMBER force fields

Helix formation is of great significance in protein folding. The helix-forming tendencies of amino acids are accumulated along the sequence to determine the helix-forming tendency of peptides. Computer simulation can be used to model this process in atomic details and give structural insights. In the current work, we employ equilibrate-state free energy simulation to systematically study the folding/unfolding thermodynamics of a series of mutated peptides. Two AMBER force fields including AMBER99SB and AMBER14SB are compared. The new 14SB force field uses refitted torsion parameters compared with 99SB and they share the same atomic charge scheme. We find that in vacuo the helix formation is mutation dependent, which reflects the different helix propensities of different amino acids. In general, there are helix formers, helix indifferent groups and helix breakers. The helical structure becomes more favored when the length of the sequence becomes longer, which arises from the formation of additional backbone hydrogen bonds in the lengthened sequence. Therefore, the helix indifferent groups and helix breakers will become helix formers in long sequences. Also, protonation-dependent helix formation is observed for ionizable groups. In 14SB, the helical structures are more stable than in 99SB and differences can be observed in their grouping schemes, especially in the helix indifferent group. In solvents, all mutations are helix indifferent due to protein–solvent interactions. The decrease in the number of backbone hydrogen bonds is the same with the increase in the number of protein–water hydrogen bonds. The 14SB in explicit solvent is able to capture the free energy minima in the helical state while 14SB in implicit solvent, 99SB in explicit solvent and 99SB in implicit solvent cannot. The helix propensities calculated under 14SB agree with the corresponding experimental values, while the 99SB results obviously deviate from the references. Hence, implicit solvent models are unable to correctly describe the thermodynamics even for the simple helix formation in isolated peptides. Well-developed force fields and explicit solvents are needed to correctly describe the protein dynamics. Aside from the free energy, differences in conformational ensemble under different force fields in different solvent models are observed. The numbers of hydrogen bonds formed under different force fields agree and they are mostly determined by the solvent model.

Effects of All-Atom Molecular Mechanics Force Fields on Amyloid Peptide Assembly: The Case of Aβ16-22 Dimer

We investigated the effects of 17 widely used atomistic molecular mechanics force fields (MMFFs) on the structures and kinetics of amyloid peptide assembly. To this end, we performed large-scale all-atom molecular dynamics simulations in explicit water on the dimer of the seven-residue fragment of the Alzheimer's amyloid-β peptide, Aβ16-22, for a total time of 0.34 ms. We compared the effects of these MMFFs by analyzing various global reaction coordinates, secondary structure contents, the fibril population, the in-register and out-of-register architectures, and the fibril formation time at 310 K. While the AMBER94, AMBER99, and AMBER12SB force fields do not predict any β-sheets, the seven force fields, AMBER96, GROMOS45a3, GROMOS53a5, GROMOS53a6, GROMOS43a1, GROMOS43a2, and GROMOS54a7, form β-sheets rapidly. In contrast, the following five force fields, AMBER99-ILDN, AMBER14SB, CHARMM22*, CHARMM36, and CHARMM36m, are the best candidates for studying amyloid peptide assembly, as they provide good balances in terms of structures and kinetics. We also investigated the assembly mechanisms of dimeric Aβ16-22 and found that the fibril formation rate is predominantly controlled by the total β-strand content.

Molecular determinant of the effects of hydrostatic pressure on protein folding stability

Hydrostatic pressure is an important environmental variable that plays an essential role in biological adaptation for many extremophilic organisms (for example, piezophiles). Increase in hydrostatic pressure, much like increase in temperature, perturbs the thermodynamic equilibrium between native and unfolded states of proteins. Experimentally, it has been observed that increase in hydrostatic pressure can both increase and decrease protein stability. These observations suggest that volume changes upon protein unfolding can be both positive and negative. The molecular details of this difference in sign of volume changes have been puzzling the field for the past 50 years. Here we present a comprehensive thermodynamic model that provides in-depth analysis of the contribution of various molecular determinants to the volume changes upon protein unfolding. Comparison with experimental data shows that the model allows quantitative predictions of volume changes upon protein unfolding, thus paving the way to proteome-wide computational comparison of proteins from different extremophilic organisms.

Proteins can be both stabilized and destabilized by pressure. Here the authors analyse the factors contributing to both negative and positive protein volume change upon denaturation, and shed light on the molecular determinants allowing proteins to be stable at high pressures.

Thermodynamics of Helix-Coil Transitions of Polyalanine in Open Carbon Nanotubes

Understanding structure formation in polypeptide chains and synthetic polymers encapsulated in pores is important in biology and nanotechnology. We present replica exchange molecular dynamics studies of the phase diagram for α-helix formation of capped polyalanine in nanotubes (NT) open to a water reservoir as a function of the NT diameter and hydrophobicity. A helix forms only in a narrow range of diameters, which surprisingly is comparable to the width of the ribosome tunnel. Increasing the hydrophobicity enhances helicity in the NT. Helix formation in polyalanine is driven by a small negative enthalpy and a positive entropy change at ≈300 K, in contrast to the large negative entropy change that destabilizes the helix and favors the coiled state in bulk water. There is an anticorrelation between water density inside the nanotube and structure formation. Confinement-induced helix formation depends on amino acid sequence. There is complete absence of helix in polyglutamine and polyserine confined to a open carbon nanotube.

Sensitivity of Folding Molecular Dynamics Simulations to Even Minor Force Field Changes

We examine the sensitivity of folding molecular dynamics simulations on the choice between three variants of the same force field (the AMBER99SB force field and its ILDN, NMR-ILDN, and STAR-ILDN variants). Using two different peptide systems (a marginally stable helical peptide and a β-hairpin) and a grand total of more than 20 μs of simulation time we show that even relatively minor force field changes can lead to appreciable differences in the peptide folding behavior.

Assessing backbone solvation effects in the conformational propensities of amino acid residues in unfolded peptides

Conformational ensembles of individual amino acid residues within model GxG peptides (x representing different amino acid residues) are dominated by a mixture of polyproline II (pPII) and β-strand like conformations. We recently discovered rather substantial differences between the enthalpic and entropic contributions to this equilibrium for different amino acid residues. Isoleucine and valine exceed all other amino acid residues in terms of their rather large enthalpic stabilization and entropic destabilization of polyproline II. In order to shed light on these underlying physical mechanisms, we performed high-level DFT calculations to explore the energetics of four representative GxG peptides where x = alanine (A), leucine (L), valine (V), and isoleucine (I) in explicit water (10 H2O molecules with a polarizable continuum water model) and in vacuo. We found that the large energetic contributions to the stabilization of pPII result, to a major extent, from peptide-water, water-water interactions, and changes of the solvent self-energy. Differences between the peptide-solvent interaction energies of hydration in pPII and β-strand peptides are particularly important for the pPII ⇌ β equilibria of the more aliphatic peptides GIG and GLG. Furthermore, we performed a vibrational analysis of the four peptides in both conformations and discovered a rather substantial mixing between water motions and peptide vibrations below 700 cm(-1). We found that the respective vibrational entropies are substantially different for the considered conformations, and their contributions to the Gibbs/Helmholtz energy stabilize β-strand conformations. Taken together, our results underscore the notion of the solvent being the predominant determinant of peptide (and protein) conformations in the unfolded state.

Importance of Hydrophilic Hydration and Intramolecular Interactions in the Thermodynamics of Helix-Coil Transition and Helix-Helix Assembly in a Deca-Alanine Peptide

For a model deca-alanine peptide the cavity (ideal hydrophobic) contribution to hydration favors the helix state over extended states and the paired helix bundle in the assembly of two helices. The energetic contributions of attractive protein-solvent interactions are separated into quasi-chemical components consisting of a short-range part arising from interactions with solvent in the first hydration shell and the remaining long-range part that is well described by a Gaussian. In the helix-coil transition, short-range attractive protein-solvent interactions outweigh hydrophobic hydration and favor the extended coil states. Analysis of enthalpic effects shows that it is the favorable hydration of the peptide backbone that favors the unfolded state. Protein intramolecular interactions favor the helix state and are decisive in favoring folding. In the pairing of two helices, the cavity contribution outweighs the short-range attractive protein-water interactions. However, long-range, protein-solvent attractive interactions can either enhance or reverse this trend depending on the mutual orientation of the helices. In helix-helix assembly, change in enthalpy arising from change in attractive protein-solvent interactions favors disassembly. In helix pairing as well, favorable protein intramolecular interactions are found to be as important as hydration effects. Overall, hydrophilic protein-solvent interactions and protein intramolecular interactions are found to play a significant role in the thermodynamics of folding and assembly in the system studied.

Coarse-Grained Protein Model Coupled with a Coarse-Grained Water Model: Molecular Dynamics Study of Polyalanine-Based Peptides

The coupling of a coarse-grained (CG) protein model with the CG water model developed by Marrink et al. (J. Phys. Chem. B 2004, 108, 750) is presented. The model was used in the molecular dynamics studies of Ac-(Ala)6-Xaa-(Ala)7-NHMe, Xaa = Ala, Leu, Val, and Gly. A Gly mutation in the middle of polyalanine is found to destabilize the helix and stabilize the hairpin by favoring a type-II' turn and probably to speed up hairpin folding. The simulations allow us to derive thermodynamic parameters of, in particular, the helical propensities (s) of amino acids in these polyalanine-based peptides. The calculated s values are 1.18 (Ala), 0.84 (Leu), 0.30 (Val), and <0.02 (Gly) at 291 K, in excellent agreement with experimental values (R(2)=0.970). Analyses using a structural approach method show that the helical propensity difference of these amino acids mainly comes from solvation effect. Leu and Val have lower helical propensities than Ala mainly because the larger side chains shield the solvation of helical structures, while Gly has a much poorer helical propensity mainly due to the much better solvation for the coil structures than for the helical structures. Overall, the model is at least about 10(2) times faster than current all-atom MD methods with explicit solvent.

Water-Centered Interpretation of Intrinsic pPII Propensities of Amino Acid Residues: In Vitro-Driven Molecular Dynamics Study

Amino acid residues of unfolded peptides in water sample only a few basins in the Ramachandran plot, including prominent polyproline II-like (pPII) conformations. Dynamics of guest residues, X, in GXG peptides in water were recently reported to be dominated by pPII and β-strand-like (β) conformations, resulting in an enthalpy-entropy compensation at ∼300 K. Using molecular dynamics (MD) in explicit solvent, we here examine pPII and β conformational ensembles of 15 guest residues in GXG peptides, quantify local orientation of water around their side chains through novel water orientation plots, and study their hydration and hydrogen bonding properties. We show that pPII and β ensembles are characterized by distinct water orientations: pPII ensembles are associated with an increased population of water oriented in parallel to the side chain surface whereas β ensembles exhibit more heterogeneous water orientations. The backbone hydration is significantly higher in pPII than in β ensembles. Importantly, pPII to β hydration differences and the solvent accessible surface area of Cβ hydrogens both correlate with experimental pPII propensities. We propose that pPII conformations are stabilized by a local, hydrogen-bonded clathrate-like water structure and that residue-specific intrinsic pPII propensities reflect distinct abilities of side chains to template this water structure.

Conformational Dynamics of Two Natively Unfolded Fragment Peptides: Comparison of the AMBER and CHARMM Force Fields

Physics-based force fields are the backbone of molecular dynamics simulations. In recent years, significant progress has been made in the assessment and improvement of commonly used force fields for describing conformational dynamics of folded proteins. However, the accuracy for the unfolded states remains unclear. The latter is however important for detailed studies of protein folding pathways, conformational transitions involving unfolded states, and dynamics of intrinsically disordered proteins. In this work, we compare the three commonly used force fields, AMBER ff99SB-ILDN, CHARMM22/CMAP, and CHARMM36, for modeling the natively unfolded fragment peptides, NTL9(1-22) and NTL9(6-17), using explicit-solvent replica-exchange molecular dynamics simulations. All three simulations show that NTL9(6-17) is completely unstructured, while NTL9(1-22) transiently samples various β-hairpin states, reminiscent of the first β-hairpin in the structure of the intact NTL9 protein. The radius of gyration of the two peptides is force field independent but likely underestimated due to the current deficiency of additive force fields. Compared to the CHARMM force fields, ff99SB-ILDN gives slightly higher β-sheet propensity and more native-like residual structures for NTL9(1-22), which may be attributed to its known β preference. Surprisingly, only two sequence-local pairs of charged residues make appreciable ionic contacts in the simulations of NTL9(1-22), which are sampled slightly more by the CHARMM force fields. Taken together, these data suggest that the current CHARMM and AMBER force fields are globally in agreement in modeling the unfolded states corresponding to β-sheet in the folded structure, while differing in details such as the native-likeness of the residual structures and interactions.

Local order in the unfolded state: conformational biases and nearest neighbor interactions

The discovery of Intrinsically Disordered Proteins, which contain significant levels of disorder yet perform complex biologically functions, as well as unwanted aggregation, has motivated numerous experimental and theoretical studies aimed at describing residue-level conformational ensembles. Multiple lines of evidence gathered over the last 15 years strongly suggest that amino acids residues display unique and restricted conformational preferences in the unfolded state of peptides and proteins, contrary to one of the basic assumptions of the canonical random coil model. To fully understand residue level order/disorder, however, one has to gain a quantitative, experimentally based picture of conformational distributions and to determine the physical basis underlying residue-level conformational biases. Here, we review the experimental, computational and bioinformatic evidence for conformational preferences of amino acid residues in (mostly short) peptides that can be utilized as suitable model systems for unfolded states of peptides and proteins. In this context particular attention is paid to the alleged high polyproline II preference of alanine. We discuss how these conformational propensities may be modulated by peptide solvent interactions and so called nearest-neighbor interactions. The relevance of conformational propensities for the protein folding problem and the understanding of IDPs is briefly discussed.

Side-chain-side-chain interactions and stability of the helical state

Understanding the driving forces that lead to the stability of the secondary motifs found in proteins, namely α-helix and β-sheet, is a major goal in structural biology. The thermodynamic stability of these repetitive units is a result of a delicate balance between many factors, which in addition to the peptide chain involves also the solvent. Despite the fact that the backbones of all amino acids are the same (except of that of proline), there are large differences in the propensity of the different amino acids to promote the helical structure. In this paper, we investigate by explicit-solvent molecular dynamics simulations the role of the side chains (modeled as coarse-grained single sites) in stabilizing α helices in an aqueous solution. Our model systems include four (six-mer-nine-mer) peptide lengths in which the magnitude of the effective attraction between the side chains is systematically increased. We find that these interactions between the side chains can induce (for the nine-mer almost completely) a transition from a coil to a helical state. This transition is found to be characterized by three states in which the intermediate state is a partially folded α-helical conformation. In the absence of any interactions between the side chains the free energy change for helix formation has a small positive value indicating that favorable contributions from the side chains are necessary to stabilize the helical conformation. Thus, the helix-coil transition is controlled by the effective potentials between the side-chain residues and the magnitude of the required attraction per residue, which is on the order of the thermal energy, reduces with the length of the peptide. Surprisingly, the plots of the population of the helical state (or the change in the free energy for helix formation) as a function of the total effective interactions between the side chains in the helical state for all peptide lengths fall on the same curve.

Systematic improvement of a classical molecular model of water

We report the iAMOEBA ("inexpensive AMOEBA") classical polarizable water model. The iAMOEBA model uses a direct approximation to describe electronic polarizability, in which the induced dipoles are determined directly from the permanent multipole electric fields and do not interact with one another. The direct approximation reduces the computational cost relative to a fully self-consistent polarizable model such as AMOEBA. The model is parameterized using ForceBalance, a systematic optimization method that simultaneously utilizes training data from experimental measurements and high-level ab initio calculations. We show that iAMOEBA is a highly accurate model for water in the solid, liquid, and gas phases, with the ability to fully capture the effects of electronic polarization and predict a comprehensive set of water properties beyond the training data set including the phase diagram. The increased accuracy of iAMOEBA over the fully polarizable AMOEBA model demonstrates ForceBalance as a method that allows the researcher to systematically improve empirical models by efficiently utilizing the available data.

Molecular dynamics simulations of a new branched antimicrobial peptide: a comparison of force fields

Branched antimicrobial peptides are promising as a new class of antibiotics displaying high activity and low toxicity and appear to work through a unique mechanism of action. We explore the structural dynamics of a covalently branched 18 amino acid peptide (referred to as B2088) in aqueous and membrane mimicking environments through molecular dynamics (MD) simulations. Towards this, we carry out conventional MD simulations and supplement these with replica exchange simulations. The simulations are carried out using four different force fields that are commonly employed for simulating biomolecular systems. These force fields are GROMOS53a6, CHARMM27 with cMAP, CHARMM27 without cMAP and AMBER99sb. The force fields are benchmarked against experimental data available from circular dichroism and nuclear magnetic resonance spectroscopies, and show that CHARMM27 without cMAP correction is the most successful in reproducing the structural dynamics of B2088 both in water and in the presence of micelles. Although the four force fields predict different structures of B2088, they all show that B2088 stabilizes against the head group of the lipid through hydrogen bonding of its Lys and Arg side chains. This leads us to hypothesize that B2088 is unlikely to penetrate into the hydrophobic region of the membrane owing to the high free energy costs of transfer from water, and possibly acts by carpeting and thus disrupting the membrane.

pH-Independence of trialanine and the effects of termini blocking in short peptides: a combined vibrational, NMR, UVCD, and molecular dynamics study

Several lines of evidence now well establish that unfolded peptides in general, and alanine in specific, have an intrinsic preference for the polyproline II (pPII) conformation. Investigation of local order in the unfolded state is, however, complicated by experimental limitations and the inherent dynamics of the system, which has in some cases yielded inconsistent results from different types of experiments. One method of studying these systems is the use of short model peptides, and specifically short alanine peptides, known for predominantly sampling pPII structure in aqueous solution. Recently, He et al. ( J. Am. Chem. Soc. 2012 , 134 , 1571 - 1576 ) proposed that unblocked tripeptides may not be suitable models for studying conformational propensities in unfolded peptides due to the presence of end effect, that is, electrostatic interactions between investigated amino acid residues and terminal charges. To determine whether changing the protonation states of the N- and C-termini influence the conformational manifold of the central amino acid residue in tripeptides, we have examined the pH-dependence of unblocked trialanine and the conformational preferences of alanine in the alanine dipeptide. To this end, we measured and globally analyzed amide I' band profiles and NMR J-coupling constants. We described conformational distributions as the superposition of two-dimensional Gaussian distributions assignable to specific subspaces of the Ramachandran plot. Results show that the conformational ensemble of trialanine as a whole, and the pPII content (χpPII = 0.84) in particular, remains practically unaffected by changing the protonation state. We found that compared to trialanine, the alanine dipeptide has slightly lower pPII content (χpPII = 0.74) and an ensemble more reminiscent of the unblocked Gly-Ala-Gly model peptide. In addition, a two-state thermodynamic analysis of the conformational sensitive Δε(T) and (3)J(H(N)H(α))(T) data obtained from electronic circular dichroism and H NMR spectra indicate that the free energy landscape of trialanine is similar in all protonation states. MD simulations for the investigated peptides corroborate this notion and show further that the hydration shell around unblocked trialanine is unaffected by the protonation/deprotonation of the C-terminal group. In contrast, the alanine dipeptide shows a reduced water density around the central residue as well as a less ordered hydration shell, which decreases the pPII propensity and reduces the lifetime of sampled conformations.

Critical Assessment of Current Force Fields. Short Peptide Test Case

The applicability of molecular dynamics simulations for studies of protein folding or intrinsically disordered proteins critically depends on quality of energetic functions-force fields. The four popular force fields for biomolecular simulations, CHARMM22/CMAP, AMBER FF03, AMBER FF99SB, and OPLS-AA/L, were compared in prediction of conformational propensities of all common proteinogenic amino acids. The minimalistic model of terminally block amino acids (dipeptides) was chosen for assessment of side chain effects on backbone propensities. The precise metadynamics simulations revealed striking inconsistency of trends in conformational preferences as manifested by investigated force fields for both backbone and side chains. To trace this disapproval between force fields, the two related AMBER force fields were studied more closely. In the cases of FF99SB and FF03, we uncovered that the distinct tends were driven by different charge models. Additionally, the effects of recent correction for side chain torsion (FF99SB-ILDN) were examined on affected amino acids and exposed significant coupling between free energy profiles and propensities of backbone and side chain conformers. These findings have important consequences for further force field development.

Membrane Protein Simulations Using AMBER Force Field and Berger Lipid Parameters

AMBER force fields are among the most commonly used in molecular dynamics (MD) simulations of proteins. Unfortunately, they lack a specific set of lipid parameters, thus limiting its use in membrane protein simulations. In order to overcome this limitation we assessed whether the widely used united-atom lipid parameters described by Berger and co-workers could be used in conjunction with AMBER force fields in simulations of membrane proteins. Thus, free energies of solvation in water and in cyclohexane, and free energies of water to cyclohexane transfer, were computed by thermodynamic integration procedures for neutral amino acid side-chains employing AMBER99, AMBER03, and OPLS-AA amino acid force fields. In addition, MD simulations of three membrane proteins in a POPC lipid bilayer, the β2 adrenergic G protein-coupled receptor, Aquaporin-1, and the outer membrane protein Omp32, were performed with the aim of comparing the AMBER99SB/Berger combination of force fields with the OPLS-AA/Berger combination. We have shown that AMBER99SB and Berger force fields are compatible, they provide reliable free energy estimations relative to experimental values, and their combination properly describes both membrane and protein structural properties. We then suggest that the AMBER99SB/Berger combination is a reliable choice for the simulation of membrane proteins, which links the easiness of ligand parametrization and the ability to reproduce secondary structure of AMBER99SB force field with the largely validated Berger lipid parameters.

50 Years of Lifson-Roig Models: Application to Molecular Simulation Data

Simple helix-coil transition theories have been indispensable tools in the analysis of data reporting on the reversible folding of α-helical polypeptides. They provide a transferable means to not only characterize different systems but to also compare different techniques, viz., experimental probes monitoring helix-coil transitions in vitro or biomolecular force fields in silico. This article addresses several issues with the application of Lifson-Roig theory to helix-coil transition data. We use computer simulation to generate two sets of ensembles for the temperature-controlled, reversible folding of the 21-residue, alanine-rich FS peptide. Ensembles differ in the rigidity of backbone bond angles and are analyzed using two distinct descriptors of helicity. The analysis unmasks an underlying phase diagram that is surprisingly complex. The complexities give rise to fitted nucleation and propagation parameters that are difficult to interpret and that are inconsistent with the distribution of isolated residues in the α-helical basin. We show that enthalpies of helix formation are more robustly determined using van't Hoff analysis of simple measures of helicity rather than fitted propagation parameters. To overcome some of these issues, we design a simple variant of the Lifson-Roig model that recovers physical interpretability of the obtained parameters by allowing bundle formation to be described in simple fashion. The relevance of our results is discussed in relation to the applicability of Lifson-Roig models to both in silico and in vitro data.

Assessment of the intrinsic conformational preferences of dipeptide amino acids in aqueous solution by combined umbrella sampling/MBAR statistics. A comparison with experimental results

The propensities of 19 amino acid dipeptides have been calculated by a distributed umbrella sampling molecular dynamics simulation procedure using the OPLS-AA force field. The potential of mean force maps was estimated with the multiple Bennett acceptance ratio statistics. The resulting propensities compare satisfactorily well with very recently published experimental data on equivalent systems. In particular, α conformation-probabilities for all of the dipeptides remain much lower than either β or P(II) propensities. This result is in agreement with most experimental data for dipeptides. However, it is also in contrast with most simulation studies performed so far with other force fields, where α conformations result even more probable than P(II) or β ones. We discuss the behavior of the OPLS-AA force field, which can be useful for the improvement of this model in reproducing the recent experimental observations on amino acid dipeptides.

Using J-coupling constants for force field validation: application to hepta-alanine

A computational solution to the protein folding problem is the holy grail of biomolecular simulation and of the corresponding force fields. The complexity of the systems used for folding simulations precludes a direct feedback between the simulations and the force fields, thus necessitating the study of simpler systems with sufficient experimental data to allow force field optimization and validation. Recent studies on short polyalanine peptides of increasing length (up to penta-alanine) indicated the presence of a systematic deviation between the experimental (NMR-derived) J-couplings and the great majority of biomolecular force fields, with the χ(2) values for even the best-performing force fields being in the 1.4-1.8 range. Here we show that by increasing the number of residues to seven and by achieving convergence through an increase of the simulation time to 2 μs, we can identify one force field (the AMBER99SB force field, out of the three force fields studied) which when compared with the experimental J-coupling data (and for a specific set of Karplus equation parameters and estimated J-coupling errors previously used in the literature) gave a value of χ(2) = 0.99, indicating that full statistical consistency between experiment and simulation is feasible. However, and as a detailed analysis of the effects of estimated errors shows, the χ(2) values may be unsuitable as indicators of the goodness of fit of the various biomolecular force fields.

Effects of different force fields and temperatures on the structural character of Abeta (12-28) peptide in aqueous solution

The aim of this work is to investigate the effects of different force fields and temperatures on the structural character of Aβ (12-28) peptide in aqueous solution. Moreover, the structural character of Aβ (12-28) peptide is compared with other amyloid peptides (such as H1 and α-syn12 peptide). The two independent temperature replica exchange molecular dynamics (T-REMD) simulations were completed by using two different models (OPLS-AA/TIP4P and GROMOS 43A1/SPC). We compared the models by analyzing the distributions of backbone dihedral angles, the secondary structure propensity, the free energy surface and the formation of β-hairpin. The results show that the mostly populated conformation state is random coil for both models. The population of β-hairpin is below 8 percent for both models. However, the peptide modeled by GROMOS 43A1 form β-hairpin with turn located at residues F19-E22, while the peptide modeled by OPLS-AA form β-hairpin with turn located at residues L17-F20.

Membrane insertion of a voltage sensor helix

Most membrane proteins contain a transmembrane (TM) domain made up of a bundle of lipid-bilayer-spanning α-helices. TM α-helices are generally composed of a core of largely hydrophobic amino acids, with basic and aromatic amino acids at each end of the helix forming interactions with the lipid headgroups and water. In contrast, the S4 helix of ion channel voltage sensor (VS) domains contains four or five basic (largely arginine) side chains along its length and yet adopts a TM orientation as part of an independently stable VS domain. Multiscale molecular dynamics simulations are used to explore how a charged TM S4 α-helix may be stabilized in a lipid bilayer, which is of relevance in the context of mechanisms of translocon-mediated insertion of S4. Free-energy profiles for insertion of the S4 helix into a phospholipid bilayer suggest that it is thermodynamically favorable for S4 to insert from water to the center of the membrane, where the helix adopts a TM orientation. This is consistent with crystal structures of Kv channels, biophysical studies of isolated VS domains in lipid bilayers, and studies of translocon-mediated S4 helix insertion. Decomposition of the free-energy profiles reveals the underlying physical basis for TM stability, whereby the preference of the hydrophobic residues of S4 to enter the bilayer dominates over the free-energy penalty for inserting charged residues, accompanied by local distortion of the bilayer and penetration of waters. We show that the unique combination of charged and hydrophobic residues in S4 allows it to insert stably into the membrane.

Size and sequence and the volume change of protein folding

The application of hydrostatic pressure generally leads to protein unfolding, implying, in accordance with Le Chatelier's principle, that the unfolded state has a smaller molar volume than the folded state. However, the origin of the volume change upon unfolding, ΔV(u), has yet to be determined. We have examined systematically the effects of protein size and sequence on the value of ΔV(u) using as a model system a series of deletion variants of the ankyrin repeat domain of the Notch receptor. The results provide strong evidence in support of the notion that the major contributing factor to pressure effects on proteins is their imperfect internal packing in the folded state. These packing defects appear to be specifically localized in the 3D structure, in contrast to the uniformly distributed effects of temperature and denaturants that depend upon hydration of exposed surface area upon unfolding. Given its local nature, the extent to which pressure globally affects protein structure can inform on the degree of cooperativity and long-range coupling intrinsic to the folded state. We also show that the energetics of the protein's conformations can significantly modulate their volumetric properties, providing further insight into protein stability.

What is the time scale for α-helix nucleation?

Helix formation is an elementary process in protein folding, influencing both the rate and mechanism of the global folding reaction. Yet, because helix formation is less cooperative than protein folding, the kinetics are often multiexponential, and the observed relaxation times are not straightforwardly related to the microscopic rates for helix nucleation and elongation. Recent ultrafast spectroscopic measurements on the peptide Ac-WAAAH(+)-NH(2) were best fit by two relaxation modes on the ∼0.1-1 ns time scale, (1) apparently much faster than had previously been experimentally inferred for helix nucleation. Here, we use replica-exchange molecular dynamics simulations with an optimized all-atom protein force field (Amber ff03w) and an accurate water model (TIP4P/2005) to study the kinetics of helix formation in this peptide. We calculate temperature-dependent microscopic rate coefficients from the simulations by treating the dynamics between helical states as a Markov process using a recently developed formalism. The fluorescence relaxation curves obtained from simulated temperature jumps are in excellent agreement with the experimentally determined results. We find that the kinetics are multiphasic but can be approximated well by a double-exponential function. The major processes contributing to the relaxation are the shrinking of helical states at the C-terminal end and a faster re-equilibration among coil states. Despite the fast observed relaxation, the helix nucleation time is estimated from our model to be 20-70 ns at 300 K, with a dependence on temperature well described by Arrhenius kinetics.

Uncovering specific electrostatic interactions in the denatured states of proteins

The stability and folding of proteins are modulated by energetically significant interactions in the denatured state that is in equilibrium with the native state. These interactions remain largely invisible to current experimental techniques, however, due to the sparse population and conformational heterogeneity of the denatured-state ensemble under folding conditions. Molecular dynamics simulations using physics-based force fields can in principle offer atomistic details of the denatured state. However, practical applications are plagued with the lack of rigorous means to validate microscopic information and deficiencies in force fields and solvent models. This study presents a method based on coupled titration and molecular dynamics sampling of the denatured state starting from the extended sequence under native conditions. The resulting denatured-state pK(a)s allow for the prediction of experimental observables such as pH- and mutation-induced stability changes. I show the capability and use of the method by investigating the electrostatic interactions in the denatured states of wild-type and K12M mutant of NTL9 protein. This study shows that the major errors in electrostatics can be identified by validating the titration properties of the fragment peptides derived from the sequence of the intact protein. Consistent with experimental evidence, our simulations show a significantly depressed pK(a) for Asp(8) in the denatured state of wild-type, which is due to a nonnative interaction between Asp(8) and Lys(12). Interestingly, the simulation also shows a nonnative interaction between Asp(8) and Glu(48) in the denatured state of the mutant. I believe the presented method is general and can be applied to extract and validate microscopic electrostatics of the entire folding energy landscape.

UV resonance Raman investigation of the conformations and lowest energy allowed electronic excited states of tri- and tetraalanine: charge transfer transitions

UV resonance Raman excitation profiles and Raman depolarization ratios were measured for trialanine and tetraalanine between 198 and 210 nm. Excitation within the pi --> pi* electronic transitions of the peptide bond results in UVRR spectra dominated by amide peptide bond vibrations. In addition to the resonance enhancement of the normal amide vibrations, we find enhancement of the symmetric terminal COO(-) vibration. The Ala(3) UVRR AmIII(3) band frequencies indicate that poly-proline II and 2.5(1) helix conformations and type II turns are present in solution. We also find that the conformation of the interior peptide bond of Ala(4) is predominantly poly-proline-II-like. The Raman excitation profiles of both Ala(3) and Ala(4) reveal a charge transfer electronic transition at 202 nm, where electron transfer occurs from the terminal nonbonding carboxylate orbital to the adjacent peptide bond pi* orbital. Raman depolarization ratio measurements support this assignment. An additional electronic transition is found in Ala(4) at 206 nm.

Intrinsic propensities of amino acid residues in GxG peptides inferred from amide I' band profiles and NMR scalar coupling constants

A reliable intrinsic propensity scale of amino acid residues is indispensable for an assessment of how local conformational distributions in the unfolded state can affect the folding of peptides and proteins. Short host-guest peptides, such as GxG tripeptides, are suitable tools for probing such propensities. To explore the conformational distributions sampled by the central amino acid residue in these motifs, we combined vibrational (IR, Raman, and VCD) with NMR spectroscopy. The data were analyzed in terms of a superposition of two-dimensional Gaussian distribution functions in the Ramachandran space pertaining to subensembles of polyproline II, beta-strand, right- and left-handed helical, and gamma-turn-like conformations. The intrinsic propensities of eight amino acid residues (x = A, V, F, L, S, E, K, and M) in GxG peptides were determined as mole fractions of these subensembles. Our results show that alanine adopts primarily (approximately 80%) a PPII-like conformation, while valine and phenylalanine were found to sample PPII and beta-strand-like conformations equally. The centers of the respective beta-strand distributions generally do not coincide with canonical values of dihedral angles of residues in parallel or antiparallel beta-strands. In fact, the distributions for most residues found in the beta-region significantly overlap the PPII-region. A comparison with earlier reported results for trivaline reveals that the terminal valines increase the beta-strand propensity of the central valine residue even further. Of the remaining investigated amino acids, methionine preferred PPII the most (0.64), and E, S, L, and K exhibit moderate (0.56-0.45) PPII propensities. Residues V, F, S, E, and L sample, to a significant extent, a region between the canonical PPII and (antiparallel) beta-strand conformations. This region coincides with the sampling reported for L and V using theoretical predictions (Tran et al. Biochemistry 2005, 44, 11369). The distributions of all investigated residues differ from coil library and computationally predicted distributions in that they do not exhibit a substantial sampling of helical conformations. We conclude that this sampling of helical conformations arises from the context dependence, for example, neighboring residues, in proteins and longer peptides, some of which is long-range.